Geodesic
On exact null controllability of Black-Scholes equation
Kybernetika, Tome 44 (2008) no. 5, pp. 685-704.

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In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with $L^2$ topology.
Classification : 45K05, 47N10, 91B28, 91G10, 93B05, 93C20, 93E03
Keywords: Black–Scholes equation; volatility; controllability; observability; Carleman estimates 
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     title = {On exact null controllability of {Black-Scholes} equation},
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     zbl = {1177.93021},
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Sakthivel, Kumarasamy; Balachandran, Krishnan; Sowrirajan, Rangarajan; Kim, Jeong-Hoon. On exact null controllability of Black-Scholes equation. Kybernetika, Tome 44 (2008) no. 5, pp. 685-704. http://geodesic.mathdoc.fr/item/KYB_2008__44_5_a5/